Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
536 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23781682 | C2 | semidirect |
| 2. #23781674 | C2 | semidirect |
| 3. #23781649 | C2 | semidirect |
| 4. #23781639 | C2 | semidirect |
| 17. C2×#41×C163 | C4 | semidirect |
| 21. C22×Q8×C163 | C4 | semidirect |
| 108. C163 | #1796 | semidirect |
| 119. C2×#41 | Dic163 | semidirect |
| 123. C22×Q8 | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781682 | 2 |
| #23781674 | 2 |
| #23781649 | 2 |
| #23781639 | 2 |
| C2×2−1+4×C163 | 2 |
| #1796 | 163 |